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The McKean model of a neuron possesses a one-dimensional fast voltagelike variable and a slow recovery variable. A recent geometric analysis of the singularly perturbed system has allowed an explicit construction of its phase response curve [S. Coombes, Physica D 160, 173 (2001)]. Here we use tools from coupled oscillator theory to study weakly coupled networks of McKean neurons. Using numerical techniques, we show that the McKean system has traveling wave phase-locked solutions consistent with that of a network of more biophysically detailed Hodgkin-Huxley neurons.

Continuum of weakly coupled oscillatory McKean neurons